Operational Resource Theory of Coherence.
TLDR
An operational theory of coherence (or of superposition) in quantum systems is established, by focusing on the optimal rate of performance of certain tasks, by demonstrating that the coherence theory is generically an irreversible theory by a simple criterion that completely characterizes all reversible states.Abstract:
We establish an operational theory of coherence (or of superposition) in quantum systems, by focusing on the optimal rate of performance of certain tasks. Namely, we introduce the two basic concepts-"coherence distillation" and "coherence cost"-in the processing quantum states under so-called incoherent operations [Baumgratz, Cramer, and Plenio, Phys. Rev. Lett. 113, 140401 (2014)]. We, then, show that, in the asymptotic limit of many copies of a state, both are given by simple single-letter formulas: the distillable coherence is given by the relative entropy of coherence (in other words, we give the relative entropy of coherence its operational interpretation), and the coherence cost by the coherence of formation, which is an optimization over convex decompositions of the state. An immediate corollary is that there exists no bound coherent state in the sense that one would need to consume coherence to create the state, but no coherence could be distilled from it. Further, we demonstrate that the coherence theory is generically an irreversible theory by a simple criterion that completely characterizes all reversible states.read more
Citations
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Quantum coherence, coherent information and information gain in quantum measurement
TL;DR: In this article, it was shown that the maximum information gain from a pure state, using a mixed apparatus is upper bounded by the initial coherence of the system and the entropy exchange between the systems and the apparatus.
Journal ArticleDOI
Coherence dynamics induced by attenuation and amplification Gaussian channels
TL;DR: In this article, the authors derived explicit expressions for the coherence depending on the parameters describing the channels, and showed that the entropy can be reduced by controlling the parameters involved, which is useful to simulate many processes in quantum thermodynamics, as finite-time driving on bosonic modes.
Journal ArticleDOI
The resource theory of coherence for quantum channels
TL;DR: In this paper, the authors defined the quantum-incoherent relative entropy of coherence of quantum channels in the framework of the resource theory by using the Choi-Jamiolkowski isomorphism.
Journal ArticleDOI
Analytically Computable Symmetric Quantum Correlations
TL;DR: In this paper, the symmetric quantum discord for two-qubit X type states and block-diagonal states and symmetric measurement induced nonlocality for any two qubit states are established on the basis of the quantum skew information.
Journal ArticleDOI
Optimal decomposition of incoherent qubit channel.
Swapan Rana,Maciej Lewenstein +1 more
TL;DR: In this paper, it was shown that any incoherent qubit channel can be decomposed into four incoherent Kraus operators by decomposing the corresponding Choi-Jamiolkowski-Sudarshan matrix.
References
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TL;DR: In this paper, Doubly Stochastic Matrices and Schur-Convex Functions are used to represent matrix functions in the context of matrix factorizations, compounds, direct products and M-matrices.
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Quantifying Coherence
TL;DR: In this article, a rigorous framework for quantification of coherence and identification of intuitive and easily computable measures for coherence has been proposed by adopting coherence as a physical resource.